在邊坡穩定性分析中，由於其簡單性和廣泛的適用性，通常採用二維（2D）分析技術，然而所有邊坡破壞本質上都是三維（3D），特別是在幾何形狀複雜的邊坡中了解其破壞機制尤為重要。進行3D邊坡穩定性分析安全係數與邊坡破壞面是更為合理的方式。在邊坡穩定性分析中，極限平衡法（LEM）和有限元法（FEM）已經被廣泛使用。LEM僅滿足靜力學方程，不考慮應變和位移兼容性使其充滿侷限性。當FEM承受較大變形時可能會導致明顯的網格變形，從而引發收斂困難，並且在邊坡破壞之前可能會計算中止，基於上述理由，邊坡的安全係數有時會出現數值誤差和不確定性問題。耦合Eulerian-Lagrangian（CEL）有限元素法可以使材料流過固定的網格，而不受網格變形的影響，本研究將其應用於三維邊坡穩定性分析中。
在這項研究中，結合使用強度折減法與CEL有限元素法於三維邊坡穩定性分析，首先使用典型的3D邊坡來驗證數值CEL FEM模型的可行性，其使用ABAQUS/Explicit。使用能量(總塑性耗散)來定義邊坡破壞，取得邊坡的安全係數，使用塑性應變來判斷破壞面的位置。
進行了幾個不同的三維幾何邊坡算例，將其給予不同的邊界條件(unrestrained、semi-restrained和fully restrianed)，將其結果的安全係數與FEM之結果進行破壞面與安全係數的對比，其中也包含了FEM不適合計算的高度非線性算例。
對比結果，在非高度非線性的情況下，FEM與CEL FEM不論是安全係數還是邊坡的破壞面結果並沒有明顯的差異，本研究證明了CEL FEM在三為邊坡穩定性分析中是個可靠的工具，其可分析FEM無法分析的高度非線性問題，能更準確地獲得安全係數與破壞面。

The slopes are 3D in nature. Therefore, the solution form 3D slope stability analysis will be more appropriate than the solution form 2D slope stability analysis. It is more reasonable to analyze the factor of safety(FOS) and slip surfaces of slope failure of the slope in 3D.There is highly nonlinear in FEM slope stability analysis , obvious mesh distortion may occur, resulting in convergence difficulty and calculation abort before slope failure. Therefore, numerical errors and uncertainties may occur. The Coupled Eulerian-Lagrangian finite element method (CEL FEM) uses fixed mesh, which without mesh deformation.
First validate a typical simple 3D slope numerical modeling using the CEL FEM combined with the shear strength-reduction technique. The FOS obtained from CEL FEM is very similar to the FOS obtained from the other method. After the validation, various types of slopes (i.e. turning corners, convex- and concave-shaped surfaces) with various boundary conditions (unrestrained, semi-restrained, and fully restrained) are carefully conducted to examine the 3D slope stability. A slope with a weak layer is an example of highly nonlinearity.
The FOS and the slip surfaces of slope failure form CEL FEM are quite similar with the result form the traditional fem. Besides, the maximum FOS difference is less 2.4%. As a conclusion, the CEL FEM in 3D slope stability analysis can obtain credible FOS and the slip surfaces of slope failure.

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